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Register a new userElectron-hole asymmetry and band gaps of commensurate double moire patterns in twisted bilayer graphene on hexagonal boron nitride
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Spontaneous orbital magnetism observed in twisted bilayer graphene (tBG) on nearly aligned hexagonal boron nitride (BN) substrate builds on top of the electronic structure resulting from combined G/G and G/BN double moire interfaces. Here we show that tBG/BN commensurate double moire patterns can be classified into two types, each favoring the narrowing of either the conduction or valence bands on average, and obtain the evolution of the bands as a function of the interlayer sliding vectors and electric fields. Finite valley Chern numbers $pm 1$ are found in a wide range of parameter space when the moire bands are isolated through gaps, while the local density of states associated to the flat bands are weakly affected by the BN substrate invariably concentrating around the AA-stacked regions of tBG. We illustrate the impact of the BN substrate for a particularly pronounced electron-hole asymmetric band structure by calculating the optical conductivities of twisted bilayer graphene near the magic angle as a function of carrier density. The band structures corresponding to other $N$-multiple commensurate moire period ratios indicate it is possible to achieve narrow width $W lesssim 30$ meV isolated folded band bundles for tBG angles $theta lesssim 1^{circ}$.
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Moire superlattices (MSL) formed in angle-aligned bilayers of van der Waals materials have become a promising platform to realize novel two-dimensional electronic states. Angle-aligned trilayer structures can form two sets of MSLs which could potentially interfere with each other. In this work, we directly image the moire patterns in both monolayer graphene aligned on hBN and twisted bilayer graphene aligned on hBN, using combined scanning microwave impedance microscopy and conductive atomic force microscopy. Correlation of the two techniques reveals the contrast mechanism for the achieved ultrahigh spatial resolution (<2 nm). We observe two sets of MSLs with different periodicities in the trilayer stack. The smaller MSL breaks the 6-fold rotational symmetry and exhibits abrupt discontinuities at the boundaries of the larger MSL. Using a rigid atomic-stacking model, we demonstrate that the hBN layer considerably modifies the MSL of twisted bilayer graphene. We further analyze its effect on the reciprocal space spectrum of the dual-moire system.
Interference of double moire patterns of graphene (G) encapsulated by hexagonal boron nitride (BN) can alter the electronic structure features near the primary/secondary Dirac points and the electron-hole symmetry introduced by a single G/BN moire pattern depending on the relative stacking arrangements of the top/bottom BN layers. We show that strong interference effects are found in nearly aligned BN/G/BN and BN/G/NB and obtain the evolution of the associated density of states as a function of moire superlattice twist angles. For equal moire periods and commensurate patterns with $Delta phi = 0^{circ}$ modulo $60^{circ}$ angle differences the patterns can add up constructively leading to large pseudogaps of about $sim 0.5$ eV on the hole side or cancel out destructively depending on their relative sliding, e.g. partially recovering electron-hole symmetry. The electronic structure of moire quasicrystals for $Delta phi =30^{circ}$ differences reveal double moire features in the density of states with almost isolated van Hove singularities where we can expect strong correlations.
Van der Waals heterostructures employing graphene and hexagonal boron nitride (hBN) crystals have emerged as a promising platform for plasmonics thanks to the tunability of their collective modes with carrier density and record values for plasmonics figures of merit. In this Article we investigate theoretically the role of moire-pattern superlattices in nearly aligned graphene on hBN by using continuum-model Hamiltonians derived from ab initio calculations. We calculate the systems energy loss function for a variety of chemical potential values that are accessible in gated devices. Our calculations reveal that the electron-hole asymmetry of the moire bands leads to a remarkable asymmetry of the plasmon dispersion between positive and negative chemical potentials, showcasing the intricate band structure and rich absorption spectrum across the secondary Dirac point gap for the hole bands.
The effect of an hexagonal boron nitride (hBN) layer close aligned with twisted bilayer graphene (TBG) is studied. At sufficiently low angles between twisted bilayer graphene and hBN, $theta_{hBN} lesssim 2^circ$, the graphene electronic structure is strongly disturbed. The width of the low energy peak in the density of states changes from $W sim 5 - 10$ meV for a decoupled system to $sim 20 - 30$ meV. Spikes in the density of states due to van Hove singularities are smoothed out. We find that for a realistic combination of the twist angle in the TBG and the twist angle between the hBN and the graphene layer the system can be described using a single moire unit cell.
We study the stability and electronic structure of magic-angle twisted bilayer graphene on the hexagonal boron nitride (TBG/BN). Full relaxation has been performed for commensurate supercells of the heterostructures with different twist angles ($theta$) and stackings between TBG and BN. We find that the slightly misaligned configuration with $theta = 0.54^circ$ and the AA/AA stacking has the globally lowest total energy due to the constructive interference of the moir{e} interlayer potentials and thus the greatly enhanced relaxation in its $1 times 1$ commensurate supercell. Gaps are opened at the Fermi level ($E_F$) for small supercells with the stackings that enable strong breaking of the $C_2$ symmetry in the atomic structure of TBG. For large supercells with $theta$ close to those of the $1 times 1$ supercells, the broadened flat bands can still be resolved from the spectral functions. The $theta = 0.54^circ$ is also identified as a critical angle for the evolution of the electronic structure with $theta$, at which the energy range of the mini-bands around $E_F$ begins to become narrower with increasing $theta$ and their gaps from the dispersive bands become wider. The discovered stablest TBG/BN with a finite $theta$ of about $0.54^circ$ and its gapped flat bands agree with recent experimental observations.
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